Question

Tony's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Tony $4.30 per pound, and type B coffee costs $5.70 per pound. This month, Tony made 177 pounds of the blend, for a total cost of $877.30. How many pounds of type A coffee did he use?

Answer 1

Tony used 94 pounds of type A coffee in his blend. We found this through creating and solving a system of equations based on the total weight and cost of the coffee blend.

Step-by-step explanation:

The student is asking for help in solving a problem involving a mixture of two types of coffee with different costs per pound. To determine how many pounds of type A coffee Tony used, we have to set up a system of equations.

Let x represent the pounds of type A coffee, and y represent the pounds of type B coffee. We have two equations based on the given information:

• The total weight of the blend: x + y = 177 pounds
• The total cost of the blend: 4.30x + 5.70y = $877.30

We can use substitution or elimination to solve this system of equations. If we solve the first equation for y (y = 177 - x), we can then substitute it into the second equation:

4.30x + 5.70(177 - x) = 877.30

This simplifies to 4.30x + 1008.90 - 5.70x = 877.30

Combining like terms, we get -1.40x = -131.60

Dividing both sides by -1.40, we find x = 94.

Therefore, Tony used 94 pounds of type A coffee in his blend.